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Stéphane Ducasse, Director of Research INRIA Lille

Random Musings − Why 12 Is a Good Number

Posted on in Categories Smalltalk

But what if, as a society, we were starting over? If we looked at all of the choices and all of the advantages and disadvantages of each, would base 10 still be the choice?

Past cultures have indeed used other systems. We likely settled on base 10 because of the practicality that we have 10 fingers to use in assisting our understanding and manipulation of those numbers.

In this age of computers and computation, it might seem that a computer like base 8 or 16 could be a good choice too; but the base 12 system seems to have a lot to offer.

Base 12

Base 12, which is also known as the duodecimal or dozenal system, has a lot of supporters who would support a move to a base 12 system.

For familiarity, we do have some systems that use 12. We have 12 hours in the day, 12 months in our year, 12 in a dozen, 12×12 (144) in a gross, 12 inches in a foot, etc. For the musically inclined, there is 12 TET—12 tone equal temperament.

What’s attractive about the dozenal system? To start with, the number 12 has six factors, namely 1, 2, 3, 4, 6 and 12. Base 10 has four: 1, 2, 5 and 10. So what does that do for us? It makes many fractions and divisions simpler and easier. For example, 1/3 in base 10 has a repeating representation of 0.33333 … .

In base 12, 1/3 is 0.4 and 1/4 is 0.3. Of course, it is not better in all fractions (1/5 = 0.24972497), so it is not better in all ways, just more.

Hold on! You might think. Base 10 lets us do great things like moving the decimal with great effect!

The good news for base 12 is that this benefit is not unique to base 10, and would work just fine in other systems including the dozenal.

On the practicality of having 10 fingers, dozenal proponents point out that (looking at your palm) your four fingers have 12 segments (phalanxes) to work with, which can be indexed by the thumb.

I found the whole idea to be intriguing and fascinating.

Here are two resources where you can find more information: